A TURBULENT ORIGIN for FLOCCULENT SPIRAL STRUCTURE in GALAXIES Bruce G

A TURBULENT ORIGIN FOR FLOCCULENT SPIRAL STRUCTURE IN GALAXIES Bruce G. Elmegreen IBM Research Division, T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598; [email protected] Debra Meloy Elmegreen Department of Physics and Astronomy, Vassar College, Poughkeepsie, NY 12604; [email protected] and Samuel N. Leitner Department of Physics, Wesleyan University, Middletown, CT 06459; [email protected] Received 2002 September 9; accepted 2003 February 16

ABSTRACT The flocculent structure of star formation in galaxies has a Fourier transform power spectrum for azimuthal intensity scans with a power-law slope that increases systematically from about 1 at large scales to about 5/3 at small scales. This is the same pattern as in the power spectra for azimuthal scans of H i emission in the Large Magellanic Clouds and for flocculent dust clouds in galactic nuclei. The steep part also corresponds to the slope of about 3 for two-dimensional power spectra that have been observed in atomic and molecular gas surveys of the Milky Way and the Large and Small Magellanic Clouds. The power-law structure for star formation in galaxies arises in both flocculent and grand-design disks, which implies that star formation is the same in each and most likely related to turbulence. The characteristic scale that separates these two slopes corresponds to several tens of pixels or several hundred parsecs in most galaxies, which is comparable to the scale height, the inverse of the Jeans wavenumber, and the size of the largest star complexes. We suggest that the power spectrum of optical light is the result of turbulence and that the large-scale turbulent motions are generated by sheared gravitational instabilities that make flocculent spiral arms first and then cascade to form clouds and clusters on smaller scales. Stellar energy sources presumably contribute to this turbulence by driving smaller scale motions and by replacing the gravitational binding energy that is released during spiral arm collapse. The spiral wave mode in the image of M81 is removed by reconstructing the Fourier transforms without the lowest 10 wavenumbers. The result shows the underlying flocculent spirals and reverse-shear spirals of star formation that are normally overwhelmed by the density wave. Subject headings: galaxies: spiral — galaxies: star clusters — ISM: structure — stars: formation — turbulence

1. INTRODUCTION and the decoupling between B-andK-band features in galaxy disks (Block & Puerari 1999), suggest that small-scale Spiral structure in galaxies is a combination of sheared star formation processes are the same everywhere, regard- features from star formation and spiral density waves in the less of the presence or lack of a spiral wave. This means that gas and stars. Most nonbarred galaxies in the field, such as if a strong wave is present and a high fraction of the star- NGC 2841 and NGC 5055, have short and patchy arms forming clouds are formed by the wave, then the star forma- (‘‘ flocculent ’’), while most galaxies with bars or nearby tion processes inside these clouds will be no different than companions, such as M81 and M51, have spiral waves or the star formation processes elsewhere. It also means that if wave modes that give them a grand design (Kormendy & there is no stellar wave, then the interstellar gas will form Norman 1979; Elmegreen & Elmegreen 1982; Elmegreen, the same total surface density of clouds by other means (see Elmegreen, & Seiden 1989). Flocculent galaxies also have review in Elmegreen 2002). small disk-to-halo mass ratios (Athanassoula, Bosma, & The nature of the star formation process itself has been elu- Papaioannou 1987; Elmegreen & Elmegreen 1990; Fuchs cidated recently through studies of geometry and kinematics. 2003), which helps explain why their spiral waves are weak Fractal-fitting procedures based on star-neighbor distribu- (Mark 1976; Thornley 1996; Kuno et al. 1997; Elmegreen tions, cell counting, and cluster hierarchies (Feitzinger & et al. 1999; Puerari et al. 2000). Braunsfurth 1984; Feitzinger & Galinski 1987; Battinelli, Star formation in grand-design galaxies is often attrib- Efremov, & Magnier 1996; Elmegreen & Salzer 1999; uted to compression from a density wave (Roberts 1969), Heydari-Malayeri et al. 2001; Pietrzynski et al. 2001), although these galaxies have no higher star formation rates unsharp masks (Elmegreen & Elmegreen 2001), and autocor- per unit gas or area than flocculent galaxies (Elmegreen & relation functions (Feitzinger & Braunsfurth 1984; Harris & Elmegreen 1986; Stark, Elmegreen, & Chance 1987). Both Zaritsky 1999; Zhang, Fall, & Whitmore 2001) show a hier- types also satisfy the Kennicutt (1998) relation between archical self-similar type of structure that often extends from average star formation rate and gas surface density. These the telescope resolution up to a kiloparsec or more. Self- observations, along with the similar star formation proper- similar structure also goes to subparsec scales in nearby ties in dwarf irregular galaxies (Hunter & Gallagher 1986) regions (Testi et al. 2000). These patterns are apparently 271 272 ELMEGREEN, ELMEGREEN, & LEITNER Vol. 590 present as long as the regions are younger than a crossing tion between star complexes and spiral arms, but it probably time (Elmegreen 2000); after this, random stellar motions cannot distinguish between different models of turbulence, smooth out the geometric structure of stellar birth. which all have similar power spectra. The hierarchical structure for star formation is similar to Optical power spectra should also give a physical scale at that in the interstellar gas, which is also fractal over a wide which star formation becomes coherent. This scale could be range of scales (Dickman, Horvath, & Margulis 1990; Scalo several hundred parsecs to a kiloparsec, corresponding to 1990; Falgarone, Phillips, & Walker 1991; Elmegreen & the disk thickness and inverse Jeans wavenumber (Zhang et Falgarone 1996; Stu¨tzki et al. 1998; Westpfahl et al. 1999; al. 2001). If this is the driving scale for the turbulence that Keel & White 2001). This similarity suggests that young stars generates star formation structures, then the source of this follow the gas as they form; some are triggered in this gas by turbulence would be the spiral instabilities that make floccu- external stellar pressures and others form spontaneously. lent arms. Turbulence driving by spiral instabilities could There is also a time and distance correlation for young stars also occur at smaller scales, followed by an inverse cascade that is similar to that for the gas (Efremov & Elmegreen in two dimensions (Wada et al. 2002), but our observations 1998). This implies that stars initially move along with the gas of features on small scales are hampered by pixel noise and andthatboththestarformationeventandthecloudlifetime a possible transition from two-dimensional to three- are limited by the transience of local gas flows (Ballesteros- dimensional turbulence in the real interstellar media of these Paredes, Hartmann, & Va´zquez-Semadeni 1999). galaxies. The origin of the kinematic and spatial correlations is In the next section, we review the suggested connections probably turbulence (Larson 1981; Falgarone & Phillips between turbulent motions and power spectra of density or 1990). Numerical simulations reproduce these features well column density. Section 3 shows the normalized power spec- and also show how stars might form spontaneously in a trum of H i emission from the LMC, multiplied by k5/3 to turbulent medium (Klessen, Heitsch, & Mac Low 2000; flatten the power-law part for easier interpretation. Then Ossenkopf, Klessen, & Heitsch 2001; Klessen 2001; Padoan Section 4 describes our galaxy data, x 5 shows power spectra et al. 2001a; Padoan & Nordlund 2002). of optical emission from these galaxies, and x 6 discusses the Interstellar turbulence can arise from a combination of likely energy sources for the turbulence that gives star for- spiral-forming instabilities driven by the swing-amplifier mation its structure. In x 7, we remove the lowest Fourier (Toomre & Kalnajs 1991; Thomasson, Donner, & components from the grand-design galaxy, M81, and show Elmegreen 1991; de Vega, Sanchez, & Combes 1996; Fuchs that the star formation patterns resemble those in a floccu- & von Linden 1998; Semelin & Combes 2000; Crosthwaite, lent galaxy, aside from the obvious orbit crowding and Turner, & Ho 2000; Bertin & Lodato 2001; Wada & reverse shear that accompanies the density wave. The results Norman 2001; Wada, Meurer, & Norman 2002; Huber & are summarized in x 8. Pfenniger 2001a, 2001b, 2002; Vollmer & Beckert 2002; A second paper (Elmegreen et al. 2003) determines the Chavanis 2002) and stellar pressures (Norman & Ferrara optical power spectra for another galaxy, M33, which has a 1996; Avila-Reese & Va´zquez-Semadeni 2001). Spiral insta- larger dynamic range for power-law analysis than the cur- bilities in the gas pump gravitational binding energy and rent sample because of its smaller distance. This second shear energy into turbulent motions over a wide range of paper also models the result in an attempt to explain the scales. Stellar pressures may generate turbulence only entire spectrum, rather than just the k5/3 part that is locally (Braun 1999; Va´zquez-Semadeni & Garcıá 2001). emphasized here. Magnetic instabilities can also generate turbulence (Asseo et al. 1978; Sellwood & Balbus 1999), but they generally do not produce dense cloudy structures by themselves. 2. DENSITY POWER SPECTRA AND TURBULENCE If spiral-forming instabilities drive the turbulence and One way to observe the correlated structure in a turbulent compression that make star-forming clouds and if this tur- gas is with a Fourier transform power spectrum, which is bulence also produces correlated structures that eventually the sum of the squares of the real and imaginary parts of the show up in young star fields, then flocculent spiral structure Fourier transform of the emission, plotted as a function of in galaxies should have the same geometric properties as the spatial frequency, k. For two or three dimensions, the local interstellar clouds. If star formation processes are also spatial frequency is the quadratic sum of the spatial frequen- independent of stellar spiral waves, then the star-forming cies in each direction. The two-dimensional power spectra parts of a grand-design galaxy should have the same of Milky Way H i emission (Crovisier & Dickey 1983; Green intrinsic geometry as flocculent spirals. 1993; Dickey et al. 2001), H i absorption (Deshpande, This paper measures the Fourier transform power spectra Dwarakanath, & Goss 2000), CO (Stu¨tzki et al. 1998), and of optical light in six galaxies and compares them with the IRAS 100 lm emission (Gautier et al. 1992; Schlegel, power spectra of H i emission from the LMC. The spectra Finkbeiner, & Davis 1998) are power laws with slopes of are very similar, suggesting that star formation follows a 2.8 to 3. The same power laws were found for two- turbulent gas. Optical light is more complex than H i emis- dimensional H i emission from the Small and Large sion, however; because dust and bright stars dominate the Magellanic Clouds (Stanimirovic et al. 1999; Elmegreen, high spatial frequencies, stars have a mixture of ages, and Kim, & Staveley-Smith 2001) and for dust emission from there is no velocity information. Nevertheless, optical pass- the Small Magellanic Cloud (Stanimirovic et al. 2000). bands have much higher spatial resolution than radio. CCD Power spectrum analyses of data cubes require special images are available for most galaxies, and most of the care to account for sharp boundaries. For example, Dickey features they show are closer to the actual star formation et al. (2001) multiplied the emission at the edge of their sur- process than large-scale gas surveys, which have revealed vey by a Gaussian-smoothing function. One way to avoid primarily the low- or moderate-density phases so far. Thus this problem is with the delta variance technique (Stu¨tzki et the power spectrum of optical light might reveal a connec- al. 1998; Zielinsky & Stu¨tzki 1999; Ossenkopf et al. 2001; No. 1, 2003 SPIRAL STRUCTURE IN GALAXIES 273

Bensch, Stu¨tzki, & Ossenkopf 2001), which does not try to gravitating, nonmagnetic gas with star formation and fit a periodic function to the data. Coriolis forces (representing a 300 pc piece of a galaxy) and For galaxies, the two-dimensional Fourier transform has got the predicted power spectrum for thin slices and the an additional problem in that it includes the structure from predicted slope variation with velocity slice thickness. the exponential disk, which is generally not wanted in an Goldman (2000) considered only the velocity-integrated analysis of interstellar clouds. For the Small Magellanic H i structure (thick-slice limit) in the SMC observations by Cloud, studied by Stanimirovic et al. (1999), this was not an Stanimirovic et al. (2000) and assumed the projected density issue because there is no disk. The LMC does have this structure (‘‘ clouds ’’) is the result of a passive response to problem, though, and for this reason, Elmegreen et al. three-dimensional incompressible turbulent motions (see also (2001) used one-dimensional Fourier transforms of the azi- Higdon 1984; Dećamp & Le Bourlot 2002). This would be muthal profiles. Azimuthal profiles are ideal for Fourier analogous to the case of a dye tracer in an incompressible tur- transforms because they are periodic and the systematic bulent fluid. In this case, the two-point correlation function radial gradients in the disk do not contribute. One- of the density is proportional to the two-point correlation dimensional power spectra have shallower slopes than two- function of the velocity, and the density power spectrum has dimensional spectra by one unit, so the azimuthal power the same slope as the velocity power spectrum. Goldman spectrum of gas emission from a galaxy becomes a power showed that the H i emission always comes from cloudy law with a slope of about 2. structures that are very thin compared with the line of sight The connection between these power spectra for intensity through the whole galaxy, and because of this the power or column density and the power spectrum of velocity fluc- spectrum of the projected structure, with its observed slope tuations associated with turbulence is not obvious. Lazarian of about 3, corresponds to a power spectrum of three- & Pogosyan (2000) showed that the structure of line emis- dimensional velocity structure that has a slope of 4 (in the sion from a turbulent gas is the result of a combination of notation above). This is slightly steeper than the three- density and velocity irregularities, with the contribution dimensional velocity structure in Kolmogorov turbulence, from each depending on the ratio of the integrated width which would have a slope of 11=3 ¼ 3:67, whereas the over the spectrum to the turbulent line width for the scale three-dimensional velocity spectrum derived by Stanimirovic observed. They considered the power spectrum for three- & Lazarian (2001) for the SMC, with its slope of 3.4, is n dimensional density alone to be Pden;3ðkÞ/k and the slightly shallower than Kolmogorov. Goldman (2000) inter- power spectrum for three-dimensional velocity alone to be preted his steep result as an effect of energy dissipation during 3m Pvel;3 / k for wavenumber k ¼ 2/ and wavelength the cascade of energy from large to small scales and noted . In this notation, Kolmogorov turbulence would have that observations by Roy & Joncas (1985) and simulations m ¼ 2/3. In the case of a shallow density spectrum, where by Vazquez-Semadeni, Ballesteros-Paredes, & Rodriguez n < 3, the power spectrum of the projected two-dimensional (1997) got this result too. A medium consisting entirely of nþm=2 line emission varies from Pem;2 / k for a thin slice of shock fronts would have a velocity power spectrum of the the velocity spectrum (i.e., a single-velocity channel width) same slope (Va´zquez-Semadeni et al. 2000). to a steeper function, /kn, for a slice that is wider than the Goldman (2002) also found that the power spectrum of velocity dispersion on the scale 1/k. In the case of a steep density in his model steepens by one unit when the inverse density spectrum, n > 3, the two-dimensional projected wavenumber scale becomes smaller than the cloud layer power spectrum varies from a different thin-slice limit, thickness, L. This implies that the two-dimensional power 3þm=2 Pem;2 / k , to a steeper thick-slice function, spectrum of density for a passive scalar in a Kolmogorov / k3m=2, to the same very thick slice limit, /kn. In both turbulent fluid should have a slope of 8/3 for transverse cases, the thick-slice limit has the same projected two- scales larger than the thickness, where k < 1/L, and a slope dimensional power spectrum as the pure density spectrum of 11/3 for transverse scales smaller than the thickness, in three dimensions. Also in both cases the shallowness of where k > 1/L. One-dimensional strips through such a the thin-slice limit implies that there is a lot of small-scale medium would therefore have power spectrum slopes that projected structure in velocity channels that is purely the steepen from 5/3 on large scales to 8/3 on small scales, result of velocity crowding along the line of sight, i.e., struc- i.e., differing by 1 in both cases. Goldman (2002) did not ture that has no density counterpart and therefore is not consider that this steepening would be observed in galaxies, from physical objects like ‘‘ clouds ’’ in the usual sense (see but it may have been observed already in the LMC H i emis- also Ballesteros-Paredes, Va´zquez-Semadeni, & Scalo 1999; sion (Elmegreen et al. 2001), and we attempt to observe it Pichardo et al. 2000). If there are no velocity fluctuations, here again for optical galactic emission. If it can be observed then the two-dimensional power spectrum of projected and if Goldman’s theory applies, then we have a good emission from a physically thin slab on the line of sight method for obtaining the line-of-sight thickness of a galaxy 1n (thinner than 1/k)isPden;2;slab / k , which is shallower based entirely on the transverse patterns of optical starlight than the three-dimensional density spectrum by one unit emission. (Lazarian et al. 2001). Analysis techniques other than Fourier transform power Stanimirovic & Lazarian (2001) found this predicted spectra have also been used to relate velocity and density steepness variation with slice thickness in the H i emission- structures in a turbulent medium. For example, the struc- line power spectra from the Small Magellanic Cloud, giving ture function of an extinction map of the Taurus region was n ¼ 3:3 for the pure density index and 3 m ¼3:4 for found to compare well with the structure function for veloc- the pure velocity index. This latter index is slightly different ity in supersonic turbulence (Padoan, Cambre´sy, & Langer than the power spectrum index for pure velocity in incom- 2002). This function involves the average value of the differ- pressible Kolmogorov turbulence, which is 11/3. ence between the extinction or the velocity, respectively, at Lazarian et al. (2001) also did numerical simulations of all pairs of points separated by some distance and raised to three-dimensional compressible turbulence in a self- a power. The density and velocity correspondence in this 274 ELMEGREEN, ELMEGREEN, & LEITNER Vol. 590 case was not explained, however, but it could be another and other sharp edges from ionization and stellar wind manifestation of density as a passive tracer for a type of tur- interactions. These slopes increase by 1 for one-dimensional bulence that acts in a nearly incompressible way. For exam- scans, and they can increase by 1 again if the transverse ple, Boldyrev, Nordlund, & Padoan (2002) propose a model dimension measured by 1/k is much larger than the line-of- for explaining structure functions in which turbulence is sight thickness. mostly solenoidal in the inertial (power-law) range and then becomes Burgers-like (sharp edged and shock dominated) i on small scales on which dissipation occurs; such a model 3. POWER SPECTRUM OF H IN THE LARGE makes density a passive scalar in the inertial range. Another MAGELLANIC CLOUD measure of structure is the probability distribution function The power spectrum of H i emission from azimuthal for column density, which spans a range between lognormal scans in the LMC is shown in Figure 1 (left), using data and Gaussian, depending on the number of independent from Elmegreen et al. (2001). The curves are shifted upward correlated regions on the line of sight (Va´zquez-Semadeni & for increasing galactocentric radii, as indicated. The wave- Garcıá 2001). Analysis techniques based on spectral line number on the abscissa is normalized to the maximum information, such as principal-component analyses (Brunt value, which is the same for each curve and corresponds to & Heyer 2002) or the spectral correlation function (Padoan, an image scale of 2 pixels. The power spectra for large radii Rosolowsky, & Goodman 2001), are not useful for optical cover a wider wavenumber range than the power spectra for images. small radii because the scan length is larger at larger radii so Evidently, the physical processes that give rise to the the minimum wavenumber, normalized to 1/(2 pixel), density structure of interstellar gas are not completely deter- decreases inversely with radius. A similar diagram was mined. A medium filled with numerous cool clouds that are shown in Elmegreen et al. (2001) but with an error at the moved in bulk by gravitational forces associated with highest frequency inadvertently caused by interpolation swing-amplified instabilities and by pressure forces associ- between pixels. The azimuthal scan of noise from beyond ated with star formation should have some of the properties the galaxy edge produces a power spectrum with a slope of of a passive scalar convected by independent turbulent 1, as shown by the dashed line. The slope at intermediate k motions. If this turbulence is somewhat incompressible in in each scan is about 5/3 and the slope at high k up to the inertial range, then the two-dimensional power spec- k 0:5 is about 8/3, as indicated by the straight lines at trum for projected column density can have a slope of 11/ the top of the figure. The highest wavenumbers have a slope 3to4, depending on the importance of energy losses in the of about 1 again and therefore look dominated by noise cascade to small scales and on the prevalence of shock fronts (this flattening at high k was also found by Lazarian et al.

10000 1000 100 10000 1000 100

2.94 Slope = –5/3 2.94 –8/3 2.64 2.64 2.34 2.34 2.04 2.04

1.74 1.74

1.44 10 (relative scale) 10 1.44 5/3 1.14 8 8 1.14

6 0.84 6 0.84 log Power (relative scale)

log Power*k R=0.54 kpc 4 R=0.54 kpc 4 2 2 –1 Sky outside LMC 0 Sky outside LMC 0 0.001 0.01 0.1 1 0.001 0.01 0.1 1 Relative Spatial Frequency Relative Spatial Frequency

Fig. 1.—Left: Power spectra of azimuthal profiles of H i emission from the Large Magellanic Cloud, using data from Elmegreen, Kim, & Staveley-Smith (2001). Each curve is for a different radius, as indicated. The power spectrum of the sky is shown as a dashed line for comparison. Lines with slopes of 1, 5/3, and 8/3 are overlaid. Right: Same power spectra multiplied by k5/3 to flatten the Kolmogorov part. Now the sky noise has a rising curve with a slope of 2/3, and the 8/3 slope in the original power spectrum has a slope of 1, as shown by the short decreasing lines on the right. The increase at the far right of these normalized power spectra is probably noise, since it has the same slope as the sky noise. No. 1, 2003 SPIRAL STRUCTURE IN GALAXIES 275

2001 in numerical simulations). The transition from 5/3 to 8/3 at physical scales of 100 pc was interpreted by Elmegreen et al. (2001) as an indication of the line-of-sight disk thickness, following predictions by Lazarian & Pogosyan (2000) and Goldman (2000). Padoan et al. (2001b) found a similar transition for this LMC data by using a different technique. The variations in slope for these power spectra are diffi- cult to see by eye, so we multiply each by k5/3, which has the effect of flattening the inertial range to a horizontal line. Fig- ure 1 (right) shows these normalized power spectra. The short lines near some of the spectra at high frequency have a slope of 1 in the normalized plot, which corresponds to a slope of 8/3 in the power spectrum; these lines indicate what the 5/3 to 8/3 transition should look like in a normalized one-dimensional power spectrum.

4. GALAXY DATA The galaxies in Table 1 were chosen for their diverse spiral types and because of the large number of pixels in the available images, shown in Figure 2. Most of the data were obtained from the Hubble Space Telescope (HST) on-line 2archive,1 with the exception of NGC 3031 (M81), which was obtained by J. C. Cuillandre in 1999 at the Canada- France-Hawaii Telescope (CFHT; Cuillandre et al. 2001). The HST exposures were ﬁrst combined to reduce gamma rays and improve the signal-to-noise ratio, and then they were mosaicked in IRAF. The complete images were trans- 2 formed through FV VIEWER into ASCII intensity tables Fig. 2.—Images of the galaxies used for this study. The NGC numbers and processed with a FORTRAN program. In the cases of and lengths of 1 kpc are indicated. All but NGC 3031 are ﬂocculent. NGC M81 and NGC 7742, star reduction algorithms were used to 3031 (north is down) is from J. C. Cuillandre of the CFHT; the others are eliminate some foreground stars. from the HST archives. The FORTRAN program took azimuthal intensity scans in a deprojected image at equally spaced radii around the center of each galaxy. The radial intervals (DR) are given in The azimuthal scans were sampled at 1 pixel spacing Table 1. Inclination angles were taken from the Third Refer- with no interpolation between pixels. Sample intensity ence Catalogue of Bright Galaxies (de Vaucouleurs et al. scans at the radius R ¼ 2:03 kpc in M81 are in Figure 3 1991, hereafter RC3); position angles were calculated from (bottom). Each curve is an average of 9 azimuthal scans the V3 angle of HST, as given in the FITS header, and from separated in radius by 1 pixel. The original one on the the position angle from north, as given by the RC3. left has a spike from a bright star at an azimuthal position of 926 pixel; the cleaned scan on the right has the 1 See http:// www.stsci.edu. 2 This research made use of the software package FV VIEWER, star partially removed. Most galaxy images did not have obtained from the High Energy Astrophysics Science Archive Research bright foreground stars such as M81, so they were not Center, provided by NASA’s Goddard Space Flight Center. cleaned.

TABLE 1 Galaxies

Distancec Pixel Size Pixel Size DRd Galaxy Passband Hubble Typea Arm Typeb (Mpc) (arcsec) (pc) (pc)

NGC 3031...... B SA(s)ab G 1.4 1.0 7.1 508 NGC 4414...... R SA(rs)c F 9.7 0.10 4.7 225 NGC 5055...... I, B SA(rs)bc F 7.2 0.10 3.5 167 NGC 5253...... V Im pec F 3.2 0.10 1.5 49 NGC 7217...... R (R)SA(r)ab F 16.0 0.10 7.7 308 NGC 7742...... I, V SA(r)b F 22.2 0.10 10.8 343

a From RC3. b (F) ﬂocculent; (G) grand design. c Distances from Tully 1988. d Separation between azimuthal scans in the radial direction. 276 ELMEGREEN, ELMEGREEN, & LEITNER Vol. 590

7 7

6 6 5/3 5/3

5 5

4 4

3 3

2 2

log Power and Power*k 1 log Power and Power*k 1

0 0 0.001 0.01 0.1 1 0.001 0.01 0.1 1 log Relative Spatial Frequency log Relative Spatial Frequency

220 220

200 200

180 180 Intensity Intensity

160 160

0 500 1000 1500 0 500 1000 1500 Azimuthal Pixel Azimuthal Pixel

Fig. 3.—Bottom: Average azimuthal scans of M81 at a radius of 2 kpc, with a star present on the left and the star mostly removed on the right. Each of these scans is an average of 9 pixel wide azimuthal scans that are separated by 1 pixel in radius. Top: Decreasing curve on each side is the average of nine power spectra, one for each of the azimuthal scans that goes into the average shown at the bottom. The ﬂat curves are the power spectra multiplied by the 5/3 power of the spatial frequency, or wavenumber k.

Fourier cosine and sine transforms, ÎcðkÞ and ÎsðkÞ, were our power spectra to make it easier to recognize wave taken of each intensity scan, I(h), using the direct sums, number regions where there is something like Kolmogorov turbulence. XN Figure 3 (top right) shows the power spectrum of the Î ðkÞ¼ cosð2kn=NÞIðnÞ ; ð1Þ c cleaned scan. It is nearly a smooth power law with a slope of n 1 ¼ 1.45. The curve below it is again normalized by the XN multiplicative factor of k5/3. ÎsðkÞ¼ sinð2kn=NÞIðnÞ : ð2Þ n¼1 5. POWER SPECTRA FOR SIX GALAXIES Here, N is the number of pixels in the azimuthal scan and k is the wavenumber. A fast Fourier transform algorithm was The power spectra for 13 equally spaced radii in M81 are not used because that would overly constrain the scan shown in Figure 5 (left), stacked up with increasing radius lengths. The power spectrum is the sum of the squares of toward the top. The normalized star-subtracted curve from these transforms: Figure 3 (right) is the fourth scan up from the bottom in Fig- ure 5. The other radii in M81 were corrected for obvious stars 2 2 PðkÞ¼ÎcðkÞ þ ÎsðkÞ : ð3Þ too. A star was defined algorithmically to be 1 pixel more than 1.2 times brighter than the average of the pixels around To reduce noise, the power spectra from nine adjacent azi- it. There is still some distortion in the normalized power muthal scans separated by 1 pixel in radius were averaged spectra in Figure 5 because of unresolved bright sources, together for all the results here. most of which are inside M81. Generally the normalized Figure 4 shows the azimuthal scans in M81 and NGC power spectra are approximately flat between 20 and 100 pc. 5055 as semitransparent ellipses. Each ellipse consists of the This means the original power spectra have slopes near 5/3 nine adjacent azimuthal scans that were used for the average in this wavenumber region, making them resemble density power spectra. structures from Kolmogorov turbulence or, within the The average power spectrum at the radius of the average uncertainties, Burgers turbulence (giving a slope of 2). azimuthal scan in Figure 3 (left) is shown in the panel above At large radii the normalized power spectra have slopes it as the top curve. The power spectrum is highly distorted near 2/3, as indicated by the dashed line, which means the because of the star. The curve below it is the power spectrum original power spectra have a slope of about 1. Because multiplied by k5/3. This normalization will be done for all this slope occurs in the outer parts of galaxies where the No. 1, 2003 SPIRAL STRUCTURE IN GALAXIES 277

Fig. 4.—Negative images of M81 (left) and NGC 5055, with ellipses at the radii of the azimuthal scans and power spectra intensity is weak, it is probably from a combination of noise, There is little difference in the power spectra for flocculent random positions for remote flocculent arms, and weak and grand-design galaxies. NGC 5055 is a flocculent galaxy long-range correlations. Models in Elmegreen et al. (2003) and its power spectrum in Figure 6 is similar to that of M81 fit both the 1 and 5/3 slopes for globally correlated in Figure 5 except for the strong components in M81 at low structures with a single intrinsic power spectrum slope of k, which are from the spiral density wave. 5/3. The relatively shallow part on large scales in the mod- The maximum size of the horizontal part of the normal- els is partly the result of using azimuthal scans rather than ized power spectrum is generally larger at smaller radii than linear scans; i.e., flocculent arms are poorly correlated on larger radii, where noise seems to dominate small k. Most opposite sides of the galaxy and well correlated with their galaxies have unresolved bright features that are intrinsic to immediate neighbors on the same side. The models also the galaxy, in addition to faint foreground stars, and these show a resolution effect in which the extended 5/3 part distort the power spectra at high k (as in Fig. 3). Between comes partly from unresolved structures like clusters and these wavenumber limits, four galaxies have clear regions OB associations, which have a range of sizes around the where the normalized power spectra are approximately hor- 100 pc scale we measure here. izontal in these figures: M81 and NGC 4414, NGC 5055, Power spectra at 10 equally spaced radii for the other gal- and NGC 7217. These horizontal parts suggest that the non- axies are shown in Figures 6–8. NGC 5055 and NGC 7742 normalized power spectra decrease as k5/3, which is have data for two passbands. Figure 6 (left) has a three-seg- appropriate for column density structure in Kolmogorov ment line to guide the eye. The rising part of the left segment has a slope of 2/3, representing noise, the flat part in the center has a slope of 0, representing the projected density in TABLE 2 Maximum 1/ Sizes for Kolmogorov Power Law the Kolmogorov part of a power spectrum for two-dimen- k sional turbulence, and the falling part on the right has a Small Radius Large Radius slope of 1, representing the projected density in the Galaxy (pc) R/R (pc) R/R Kolmogorov part of a power spectrum for three- 25 25 dimensional turbulence. NGC 3031 (M81) ...... 500 0.1 100 0.02 The results of the power spectrum analysis are summar- NGC 4414...... 300 0.06 100 0.02 ized in Table 2, which gives the size ranges for the horizontal NGC 5055...... 1000 0.07 50 0.003 parts of the normalized power spectra in parsecs and in NGC 5253...... 60 0.03 ...... proportion to R , as indicated by the scales at the tops of NGC 7217...... 200 0.02 60 0.007 25 NGC 7742...... the figures. 278 ELMEGREEN, ELMEGREEN, & LEITNER Vol. 590

log R/R25 0.26 –0.74 –1.74 0.29 –0.71 –1.71 –2.71 Size (pc) 10000 1000 100 10000 1000 100 10

M81 NGC 4414 (relative scale) 5/3 log Power*k

3 3 2 2 1 1 0 0 0.001 0.01 0.1 1 0.001 0.01 0.1 1 Relative Spatial Frequency Relative Spatial Frequency

Fig. 5.—Normalized power spectra for M81 and NGC 4414 at different radii, increasing toward the top. The radial intervals are given in Table 1: 508 pc starting at 508 pc for M81, and 225 pc starting at 225 pc for NGC 4414. The dashed line has a slope on this figure of 2/3, which corresponds to 1 in the original power spectrum, before normalization with the factor k5/3. The scales at the top of the figure correspond to the inverse wavenumber, 1/k, and are in parsecs and fractions of the galaxy radius, R25. The scale at the bottom is the normalized wavenumber, which has k = 1/(2 pixel) at the right edge for each scan (where the normalized wavenumber is 1). The power spectra for the outer parts of M81 increase sharply at low k, by 2 orders of magnitude compared with the extrapolation from higher k. This excess power is from the spiral density wave. The power spectra for M81 at intermediate to high k, which are dominated by star formation, are about the same as for the flocculent galaxy NGC 5055. turbulence in a one-dimensional scan. Unfortunately, the bottom); unfortunately, this ring also has so many bright uncertainties from brightness variations among stars, pixel pixels that the power spectrum is distorted. Presumably the noise, and the limited power-law range make it impossible distance to NGC 7742 is too large to resolve the several hun- to distinguish between this slope and 2, for example, so we dred parsec outer scale for turbulence, so each star complex cannot specify what type of turbulence might be causing with this scale has a size of only a few tens of pixels. NGC these brightness patterns. 7217 has the same problems as NGC 7742: it is too distant The other galaxies could have the same structure but are to resolve the turbulent structures and the star formation too noisy or distant to resolve here. In only one case, NGC patches are intrinsically faint. 5055, is the pixel and intrinsic stellar noise low enough to The meaning of the length scale at the top of the fig- see a possible transition to a three-dimensional column den- ures is 1/k in the azimuthal direction. Because 1 on the sity spectrum at high frequency. This galaxy differs from the lower abscissa corresponds to a wavenumber of 1/ others in having very bright patches of well-resolved star (2 pixel), the length scale at the top is given by L ¼ 2D formation throughout the disk. NGC 7742 has faint patches divided by the normalized scale at the bottom, for pixel everywhere but in a ring of radius 800 pc, where they are size h in radians and galaxy distance D. This azimuthal bright, and there is no evidence for a k5/3 spectrum any- length is not the same as the total feature length, which, where except possibly in this ring (the third scan up from the because of shear, can be much larger if it is measured No. 1, 2003 SPIRAL STRUCTURE IN GALAXIES 279

log R/R25 –1.16 –2.16 –3.16 –1.16 –2.16 –3.16 Size (pc) 1000 100 10 1000 100 10

NGC 5055 I band NGC 5055 B band (relative scale) 5/3 log Power*k

3 3 2 2 1 1 0 0 0.001 0.01 0.1 1 0.001 0.01 0.1 1 Relative Spatial Frequency Relative Spatial Frequency

Fig. 6.—Normalized power spectra for NGC 5055 in two passbands. The radii are in increments of 167 pc. The inner regions (lower curves) have a long flat part on this diagram, suggesting optical features with the same structure as Kolmogorov turbulence. A three-segmented line illustrates this flat part, in comparison with a rising part, probably from noise, at lower wavenumber, and a falling part, which may be from the resolved line-of-sight disk thickness, at higher wavenumber. The rise at highest wavenumber has the same slope as the noise. along a spiral arm. The typical length scale in the flat correlated regions with larger sizes are so much older, red- part of our power spectra is 100 pc, with a range between der, and dimmer that they do not stand out in our optical 50 and 1000 pc, depending on galaxy and galactocentric images. A power spectrum analysis of very sensitive K-band radius. This distance is comparable to the inverse of the images might find longer range correlations. According to Jeans wavenumber in the interstellar gas, which is the time-size correlation in Efremov & Elmegreen (1998), c2=G 200 pc for velocity dispersion c ¼ 5kms1 regions 1 kpc in size, such as the Gould Belt, form stars for 2 and disk mass surface density ¼ 0:002 g cm 10 M 30 Myr, and these are still visible in our optical images. An pc2. Star formation regions much larger than this in the extrapolation of this relation to regions 10 kpc in size sug- azimuthal direction are apparently not coherent on aver- gests a formation time over 100 Myr, in which case they age (although a few individual regions might be), and should be dominated by stars of type A. Groupings of A those separated by more than this distance, such as those stars of this size may exist without detection in the optical on opposite sides of the galaxy, are independent. Star- data used here. They would be relatively smooth, dim, and forming regions smaller than 100–500 pc tend to be sheared into tight spirals. On the other hand, it is plausible correlated. that correlated regions much larger than a scale height do The maximum scale for the k5/3 part is also comparable not exist because turbulent motions parallel to the plane, to the perpendicular disk scale height. Either this height, driven by spiral instabilities, for example, cannot be much along with the Jeans length, is a true maximum scale for star larger than turbulent motions perpendicular to the plane, formation (as suggested by Efremov 1995 and others) or which would have to be driven by three-dimensional mixing 280 ELMEGREEN, ELMEGREEN, & LEITNER Vol. 590

log R/R25 –0.37 –1.37 –2.37 0.04 –0.96 –1.96 Size (pc) 1000 100 10 10000 1000 100

NGC 5253 NGC 7217 (relative scale) 5/3 log Power*k

3 3 2 2 1 1 0 0 0.001 0.01 0.1 1 0.001 0.01 0.1 1 Relative Spatial Frequency Relative Spatial Frequency

Fig. 7.—Normalized power spectra for NGC 5253 and NGC 7217 at radial intervals of 49 and 308 pc. The innermost regions (lower curves) have parts with power spectra similar to that of Kolmogorov turbulence. of the in-plane motions. A fixed ratio for these two speeds This origin of structure on the Jeans length also implies was suggested in simulations of spiral instabilities by Huber that much of the interstellar turbulence is from gravitational & Pfenniger (2001a). instabilities in the gas. This is consistent with recent numerical experiments (see references in x 1). The turbulent energy comes directly from the gravitational binding energy of the gas layer. This is not a renewable energy source because col- 6. ENERGY SOURCE FOR INTERSTELLAR lapse dissipates energy by radiation, so ultimately the TURBULENCE energy of turbulence has to come from shear or stars. Shear If the gravitational Jeans length or the scale height in the is not important on the scale of individual clouds because ambient medium is the typical scale for coherent, star- most of them are denser than the gravitational tidal density forming structures, then the implication is that gaseous (¼ 3A=G for Oort A and angular rate ), so they cannot self-gravity initiates the formation of star-forming clouds, be broken apart by shear. This is unlike the case for whole producing star complexes. A turbulent cascade to smaller flocculent spirals, which are easily stretched by shear. scales forms smaller clouds and smaller stellar conglomer- Numerical simulations with only self-gravity and shear get ates, such as OB associations and subgroups, while shear renewable spirals for this reason (Toomre & Kalnajs 1991; stretches the complexes on larger scales into flocculent Sellwood & Carlberg 1984; Semelin & Combes 2000; Huber spirals. This is beginning to be the standard model for star & Pfenniger 2002), but analogous simulations in which formation, but now it has the additional aspect that all dense clouds form cannot break these clouds apart without resolvable scales inside the unstable wavelength are something like star formation and young stellar pres- hierarchically fractal for both the gas and the stars. sures (Huber & Pfenniger 2001a; Wada & Norman 2001). No. 1, 2003 SPIRAL STRUCTURE IN GALAXIES 281

log R/R25 0.25 –0.75 –1.75 0.25 –0.75 –1.75 Size (pc) 10000 1000 100 10000 1000 100

NGC 7742 I band NGC 7742 V band (relative scale) 5/3 log Power*k

3 3 2 2 1 1 0 0 0.001 0.01 0.1 1 0.001 0.01 0.1 1 Relative Spatial Frequency Relative Spatial Frequency

Fig. 8.—Normalized power spectra for NGC 7742 in two passbands. The radii are in increments of 343 pc. There is no indication of Kolmogorov turbulence in the optical structure of this galaxy.

Viscosity from cloud-cloud interactions in the presence of strongly compress the gas. Stellar power is hotter and more shear can also break apart spiral instabilities (Vollmer & localized, producing ionized and hot uniform cavities with Beckert 2002). cloudy debris at the edge in a turbulent shell or layer. The The energy liberated by continuous spiral instabilities is primary role of stellar energy on a large scale is to provide important as a source of turbulence in the interstellar internal energy that reverses the cold collapse of cloud and medium (ISM; e.g., Vollmer & Beckert 2002; Wada et al. star formation, thereby maintaining a steady state in the 2002). The power density is approximately the ISM energy presence of continuous spiral instabilities. density c2 multiplied by the instability growth rate, G=c, Spiral instabilities can also move cold clouds around which amounts to 2 1027 ergs cm3 s1 in the solar neigh- without much feedback from them in the form of pressure borhood. This power input is important because the spiral gradients. This can produce a type of structure that is analo- growth time is comparable to the crossing time over the disk gous to a passive scalar in laboratory Kolmogorov turbu- thickness, and this is about equal to the energy dissipation lence. The sharp edges in these cold clouds that are time from shocks and turbulent decay. The energy is compa- produced by ionization and stellar winds can steepen a rable to that from supernovae at a rate of 1 per 100 yr in a three-dimensional density power spectrum from 11/3 to whole galaxy, assuming a 1% eﬃciency for converting the 4, as discussed in x 2, but such sharp edges are not likely to explosion energy into ISM motions. Both spiral instabilities show up in the stars unless very young regions are observed, and stars provide enough power to interstellar turbulence as in the compressed ridge of Orion (Reipurth, Rodriguez, and cloud formation, but spiral instabilities may be preferred & Chini 1999). Thus we obtain something like the because they are pervasive, large-scale, and cold, which Kolmogorov 5/3 slope here (for one-dimensional scans in allows the gravity-driven motions to be supersonic and the projected distribution of a passive scalar) even though 282 ELMEGREEN, ELMEGREEN, & LEITNER Vol. 590 many of the stars in the optical images may have been triggered along sharp fronts by nearby high pressures.

7. FLOCCULENT SPIRALS INSIDE THE GRAND-DESIGN GALAXY M81 Figure 9 shows the galaxy M81 without the 10 lowest Fourier components. A few bright stars have also been removed. The remaining part of the galaxy image lies mostly in the power-law region of the power spectrum. The star formation features are patchy, sheared spirals that resemble flocculent spirals in other galaxies. They tend to be concentrated in the density wave spiral arms (see Fig. 4) because of the flow pattern, which moves the gas more slowly through the arms than the interarm regions. The flow also has an arm region with reverse shear, which gives some of the patches larger pitch angles than the arms (Balbus 1988; Kim & Ostriker 2001). Nevertheless, the intrinsic structure of these star-forming patches is hierarchical and self-similar, as indicated by the power spectrum, so the star formation process inside them is more closely related to turbulence than to spiral waves. The detailed star formation processes are therefore the same in flocculent and grand-design galaxies.

8. DISCUSSION The spiral arms in flocculent galaxies and the star formation patches in grand-design galaxies appear to be the largest optical features generated by turbulence with a nearly Kolmogorov scaling law. The similarity between the azimuthal sizes of these regions and the inverse of the crit- ical Jeans wavenumber suggests they form by gravitational instabilities in the ambient gas. In the presence of shear Fig. 9.—Image of M81 (north is down) with the lowest 10 wavenumbers these instabilities compress and twist the gas into flocculent removed (k ¼ 1, 2, ..., 10). The bright features are star formation regions, spiral arms, and they also generate supersonic turbulence, and the dark features are dust or low-intensity disk regions. Several bright foreground stars have been removed. The star formation structure in this which cascades to smaller scales, making a hierarchy of image is flocculent and similar to that of NGC 5055, although for M81 it is cloud and star formation structures. The reverse process of concentrated in the regions of the spiral density wave arms. cloud destruction, which is required to ensure a steady state, is the role of star formation. The pressures associated with star formation also contribute to small-scale turbulence. due to inverse cascade on scales larger than the driving scale Hierarchical structures for star formation have not yet of 10 pc, which was from self-gravity in the cold gas compo- been found in numerical simulations of galaxies or clouds, nent. Some of the power-law range for structure observed although this feature of turbulent gas alone has been optically here could be from an inverse cascade too, but the simulated by several groups (MacLow & Ossenkopf 2000; difference between this process and stretching from shear is Klessen 2000; Ossenkopf et al. 2001; Ostriker, Stone, & not clear from the two-dimensional analysis in Wada et al., Gammie 2001). Hierarchical structure in collapsing gas was and the importance of shear has been minimized in our simulated by Semelin & Combes (2000), Huber & Pfenniger study by considering only the azimuthal profiles for the (2001a, 2002), and Chavanis (2002). The simulations that power spectra. The importance of inverse cascades in are most relevant to what we find here were by Huber & galaxies with a scale height larger than the Jeans length in Pfenniger (2001a), who got a fractal mass-size correlation in the cold component is also not clear. the spirals generated by gravitational instabilities in sheared gaseous disks, although their dynamic range was small. HST archival images were prepared by the staff at the Wada & Norman (2001) also got chaotic spirals from disk Space Telescope Science Institute for NASA under contract instabilities; their effective driving length was 200 pc, simi- NAS 5-26555. We are grateful to J.-C. Cuillandre for the lar to that observed here, but these authors did not analyze image of M81. Funding for one of us (S. N. L.) was pro- the correlations in their gas or star formation structures. vided by the Keck Northeast Astronomy Consortium for The turbulent spirals in two-dimensional simulations by summer work at Vassar College. B. G. E is supported by Wada et al. (2002) were found to have a two-dimensional NSF grant AST 02-05097. We are grateful to the referee for energy power spectrum with a power-law slope of about 1 helpful suggestions. No. 1, 2003 SPIRAL STRUCTURE IN GALAXIES 283

REFERENCES Asseo, E., Cesarsky, C. J., Lachieze-Ray, M., & Pellat, R. 1978, ApJ, 225, Hunter, D. A., & Gallagher, J. S., III. 1986, PASP, 98, 5 L21 Keel, W. C., & White, R. E., III. 2001, AJ, 121, 1442 Athanassoula, E., Bosma, A., & Papaioannou, S. 1987, A&A, 179, 23 Kennicutt, R. C. 1998, ApJ, 498, 541 Avila-Reese, V., & Va´zquez-Semadeni, E. 2001, ApJ, 553, 645 Kim, W.-T., & Ostriker, E. C. 2001, ApJ, 559, 70 Balbus, S. A. 1988, ApJ, 324, 60 Klessen, R. S. 2000, ApJ, 535, 869 Ballesteros-Paredes, J., Hartmann, L., & Va´zquez-Semadeni, E. 1999, ApJ, ———. 2001, ApJ, 556, 837 527, 285 Klessen, R. S., Heitsch, F., & Mac Low, M.-M. 2000, ApJ, 535, 887 Ballesteros-Paredes, J., Va´zquez-Semadeni, E., & Scalo, J. 1999, ApJ, 515, Kormendy, J., & Norman, C. A. 1979, ApJ, 233, 539 286 Kuno, N., Tosaki, T., Nakai, N., & Nishiyama, K. 1997, PASJ, 49, 275 Battinelli, P., Efremov, Y., & Magnier, E. A. 1996, A&A, 314, 51 Larson, R. B. 1981, MNRAS, 194, 809 Bensch, F., Stu¨tzki, J., & Ossenkopf, V. 2001, A&A, 366, 636 Lazarian, A., & Pogosyan, D. 2000, ApJ, 537, 720 Bertin, G., & Lodato, G. 2001, A&A, 370, 342 Lazarian, A., Pogosyan, D., Va´zquez-Semadeni, E., & Pichardo, B. 2001, Block, D. L., & Puerari, I. 1999, A&A, 342, 627 ApJ, 555, 130 Boldyrev, S., Nordlund, A., & Padoan, P. 2002, ApJ, 573, 678 MacLow, M.-M., & Ossenkopf, V. 2000, A&A, 353, 339 Braun, R. 1999, in Proc. 2nd Guillermo Haro Conference, Interstellar Mark, J. W. K. 1976, ApJ, 205, 363 Turbulence, ed. J. Franco & A. Carraminana (Cambridge: Cambridge Norman, C. A., & Ferrara, A. 1996, ApJ, 467, 280 Univ. Press), 12 Ossenkopf, V., Klessen, R. S., & Heitsch, F. 2001, A&A, 379, 1005 Brunt, C. M., & Heyer, M. H. 2002, ApJ, 566, 289 Ostriker, E. C., Stone, J. M., & Gammie, C. F. 2001, ApJ, 546, 980 Chavanis, P. H. 2002, A&A, 381, 340 Padoan, P., Cambre´sy, L., & Langer, W. 2002, ApJ, 580, L57 Crosthwaite, L. P., Turner, J. L., & Ho, P. T. P. 2000, AJ, 119, 1720 Padoan, P., Juvela, M., Goodman, A. A., & Nordlund, A. 2001a, ApJ, 553, Crovisier, J., & Dickey, J. M. 1983, A&A, 122, 282 227 Cuillandre, J.-C., et al. 2001, in ASP Conf. Ser. 232, The New Era of Wide Padoan, P., Kim, S., Goodman, A., & Staveley-Smith, L. 2001b, ApJ, 555, Field Astronomy, ed. R. Clowes, A. Adamson, & G. Bromage (San L33 Francisco: ASP), 398 Padoan, P., & Nordlund, A. 2002, ApJ, 576, 870 Dećamp, N., & Le Bourlot, J. 2002, A&A, 389, 1055 Padoan, P., Rosolowsky, E. W., & Goodman, A. A. 2001, ApJ, 547, 862 Deshpande, A. A., Dwarakanath, K. S., & Goss, W. M. 2000, ApJ, 543, Pichardo, B., Va´zquez-Semadeni, E., Gazol, A., Passot, T., & Ballesteros- 227 Paredes, J. 2000, ApJ, 532, 353 de Vaucouleurs, G., de Vaucouleurs, A., Corwin, H. G., Jr., Buta, R. J., Pietrzynski, G., Gieren, W., Fouque´, P., & Pont, F. 2001, A&A, 371, 497 Paturel, G., & Fouque´, P. 1991, Third Reference Catalogue of Bright Puerari, I., Block, D. L., Elmegreen, B. G., Frogel, J. A., & Eskridge, P. B. Galaxies (New York: Springer) (RC3) 2000, A&A, 359, 932 de Vega, H. J., Sanchez, N., & Combes, F. 1996, Nature, 383, 56 Reipurth, B., Rodriguez, L. F., & Chini, R. 1999, AJ, 118, 983 Dickey, J. M., McClure-Griffiths, N. M., Stanimirovic, S., Gaensler, B. M., Roberts, W. W. 1969, ApJ, 158, 123 & Green, A. J. 2001, ApJ, 561, 264 Roy, J.-R., & Joncas, G. 1985, ApJ, 288, 142 Dickman, R. L., Horvath, M. A., & Margulis, M. 1990, ApJ, 365, 586 Scalo, J. 1990, in Physical Processes in Fragmentation and Star Formation, Efremov, Y. N. 1995, AJ, 110, 2757 ed. R. Capuzzo-Dolcetta, C. Chiosi, & A. Di Fazio (Dordrecht: Kluwer), Efremov, Y. N., & Elmegreen, B. G. 1998, MNRAS, 299, 588 151 Elmegreen, B. G. 2000, ApJ, 530, 277 Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525 ———. 2002, ApJ, 577, 206 Sellwood, J. A., & Balbus, S. A. 1999, ApJ, 511, 660 Elmegreen, B. G., & Elmegreen, D. M. 1986, ApJ, 311, 554 Sellwood, J. A., & Carlberg, R. G. 1984, ApJ, 282, 61 ———. 2001, AJ, 121, 1507 Semelin, B., & Combes, F. 2000, A&A, 360, 1096 Elmegreen, B. G., Elmegreen, D. M., & Seiden, P. E. 1989, ApJ, 343, 602 Stanimirovic, S., & Lazarian, A. 2001, ApJ, 551, L53 Elmegreen, B. G., & Falgarone, E. 1996, ApJ, 471, 816 Stanimirovic, S., Staveley-Smith, L., Dickey, J. M., Sault, R. J., & Elmegreen, B. G., Kim, S., & Staveley-Smith, L. 2001, ApJ, 548, 749 Snowden, S. L. 1999, MNRAS, 302, 417 Elmegreen, B. G., Leitner, S. N., Elmegreen, D. M., & Cuillandre, J.-C. Stanimirovic, S., Staveley-Smith, L., van der Hulst, J. M., Bontekoe, Tj. R., 2003, ApJ, submitted Kester, D. J. M., & Jones, P. A. 2000, MNRAS, 315, 791 Elmegreen, D. M., Chromey, F. R., Bissell, B. A., & Corrado, K. 1999, AJ, Stark, A. A., Elmegreen, B. G., & Chance, D. 1987, ApJ, 322, 64 118, 2618 Stu¨tzki, J., Bensch, F., Heithausen, A., Ossenkopf, V., & Zielinsky, M. Elmegreen, D. M., & Elmegreen, B. G. 1982, MNRAS, 201, 1021 1998, A&A, 336, 697 ———. 1990, ApJ, 364, 412 Testi, L., Sargent, A. I., Olmi, L., & Onello, J. S. 2000, ApJ, 540, L53 Elmegreen, D. M., & Salzer, J. J. 1999, AJ, 117, 764 Thomasson, M., Donner, K. J., & Elmegreen, B. G. 1991, A&A, 250, 316 Falgarone, E., & Phillips, T. 1990, ApJ, 359, 344 Thornley, M. D. 1996, ApJ, 469, L45 Falgarone, E., Phillips, T. G., & Walker, C. K. 1991, ApJ, 378, 186 Toomre, A., & Kalnajs, A. J. 1991, in Dynamics of Disk Galaxies, ed. Feitzinger, J. V., & Braunsfurth, E. 1984, A&A, 139, 104 B. Sundelius (Go¨teborg: Univ. Chalmers Press), 341 Feitzinger, J. V., & Galinski, T. 1987, A&A, 179, 249 Tully, R. B. 1988, Catalog of Nearby Galaxies (Cambridge: Cambridge Fuchs, B. 2003, in The Evolution of Galaxies III: From Simple Approaches Univ. Press) to Self-consistent Models, ed. G. Hensler & G. Stasinska (Dordrecht: Va´zquez-Semadeni, E., Ballesteros-Paredes, J., & Rodriguez, L. F. 1997, Kluwer), in press ApJ, 474, 292 Fuchs, B., & von Linden, S. 1998, MNRAS, 294, 513 Va´zquez-Semadeni, E., & Garcıá, N. 2001, ApJ, 557, 727 Gautier, T. N., Boulanger, F., Perault, M., & Puget, J. L. 1992, AJ, 103, Va´zquez-Semadeni, E., Ostriker, E. C., Passot, T., Gammie, C., & Stone, J. 1313 2000, in Protostars and Planets IV, ed. V. Mannings, A. Boss, & Goldman, I. 2000, ApJ, 541, 701 S. Russell (Tucson: Univ. Arizona Press), 3 Green, D. A. 1993, MNRAS, 262, 327 Vollmer, B., & Beckert, T. 2002, A&A, 382, 872 Harris, J., & Zaritsky, D. 1999, AJ, 117, 2831 Wada, K., Meurer, G., & Norman, C. A. 2002, ApJ, 577, 197 Heydari-Malayeri, M., Charmandaris, V., Deharveng, L., Rosa, M. R., Wada, K., & Norman, C. A. 2001, ApJ, 547, 172 Schaerer, D., & Zinnecker, H. 2001, A&A, 372, 495 Westpfahl, D. J., Coleman, P. H., Alexander, J., & Tongue, T. 1999, AJ, Higdon, J. C. 1984, ApJ, 285, 109 117, 868 Huber, D., & Pfenniger, D. 2001a, A&A, 374, 465 Zhang, Q., Fall, S. M., & Whitmore, B. C. 2001, ApJ, 561, 727 ———. 2001b, Ap&SS, 276, 523 Zielinsky, M., & Stu¨tzki, J. 1999, A&A, 347, 630 ———. 2002, A&A, 386, 359